Josh Brownhill scores the only goal of the game for Bristol City against Huddersfield.
Photograph: Toby Melville/Reuters

There is no respite for David Wagner and Huddersfield. Anchored to the bottom of the Premier League and eight points adrift of the last safe spot, they fell to a ninth successive defeat as they were dumped out of the FA Cup by Bristol City courtesy of a goal scored against the run of play by Josh Brownhill.

Wagner’s side had their chances early in the second half but they were punished for their profligacy when Brownhill produced a lovely piece of skill in the Huddersfield area to create room for a left-foot shot that beat Ben Hamer at his near post.

It was a goal that extended the Championship club’s unbeaten run to nine matches, secured their place in the fourth round and piled the misery on Huddersfield, who appear to be in freefall.

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Scoring goals has been a problem for Huddersfield all season and nothing changed on a bitterly cold evening in the West Country, where Wagner’s side were toothless in attack. Steve Mounié and Alex Pritchard, who both came off the bench at half-time, failed to take presentable chances. Chris Löwe dragged another opportunity wide of the far post and Jonathan Hogg wastefully thrashed wide.

Bristol City, who had hit the bar in the first half through Callum O’Dowda, were not so forgiving. Brownhill’s dexterous footwork – it was a terrific Cruyff turn – bamboozled the Huddersfield defence and, in truth, it was hard to see Wagner’s team responding once they fell behind, which is perhaps not surprising given their dismal run of form.

Wagner sounded bitterly disappointed. “We were not good today, the performance was not the level we are capable of,” said the Huddersfield manager, who made eight changes to his starting XI, including giving a debut to Jason Puncheon.

“The first half I was anything but happy with the way we defended. I think second half we were better. We had enough opportunities to score, to give the goalkeeper some work to do. We had good positions in the box – shots where we didn’t hit the target, which is a problem that we have had over the whole season. Then we conceded a goal from a situation where I think we had much better situations to score.”

Reflecting on the wider malaise that has set in, Wagner added: “We have another defeat, this hurts. We wanted to have this winning feeling back, which we haven’t had now for such a long period. Nine defeats in a row means we have had nine games without a clean sheet. That is not good enough and this means we have not scored enough goals as well, so we have problems at both ends of the pitch, which we have to solve.”

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To rub salt into Huddersfield’s wounds, Bristol City came into this game in a state of disarray off the field because of a sickness bug that Lee Johnson said forced him to “change the team about 15 times in 48 hours”.Johnson claimed that “four or five players were in bed ill”, three of the substitutes were in no state to come on and Adam Webster played despite losing 4kg as a result of the virus that has swept through the squad.

In truth, everyone looked off colour in a banal opening 45 minutes that produced little in the way of goalmouth action at either end of the pitch. O’Dowda’s header hit the bar and Laurent Depoitre came close to turning in a cross from Erik Durm for Huddersfield but that was about as good as it got before the interval.

Then came that flurry of Huddersfield chances, with the pick of them probably being the lob that Mounié lifted over the head of Niki Mäenpää, the Bristol City goalkeeper, after running through one-on-one, only for Bailey Wright to get back and hack clear.

It was left to Brownhill to deliver the classic sucker-punch at the other end as Bristol City, who reached the semi-finals of the Carabao Cup last season, celebrated their fifth victory over Premier League opponents in 17 months.

“It would be nice to have another big team here in the next round,” added Johnson. “If you could give me a choice, I’d say Tottenham or Liverpool.”